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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Transport of a quantum particle in a dimer under the influence of two correlated dichotomic colored noises

A. Fuliński, Paweł Góra

Published Nov 1, 1993• 12 citations
Publisher

Abstract

The transport of a quantum particle in a dimer is investigated for the case in which the influence of phonons from different branches is modeled by a dichotomic stochastic process with exponentially decaying correlations. For physical reasons, these processes might be correlated. An exact equation for the correlations between matrix elements of the density operator and both stochastic processes is constructed, and eigenvalues of the corresponding matrix are found numerically. Correlations between the noises reduce the range of incoherent transport. Various criteria for distinguishing between coherent and incoherent motion are also discussed.

DOI
10.1103/physreve.48.3510

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The transport of a quantum particle in a dimer is investigated for the case in which the influence of phonons from different branches is modeled by a dichotomic stochastic process with exponentially decaying correlations. For physical reasons, these processes might be correlated. An exact equation for the correlations between matrix elements of the density operator and both stochastic processes is constructed, and eigenvalues of the corresponding matrix are found numerically. Correlations between the noises reduce the range of incoherent transport. Various criteria for distinguishing between coherent and incoherent motion are also discussed.
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We obtain kinetic equations for the stochastically averaged reduced density matrix of a quantum system driven by a dichotomous Markovian process and weakly coupled to a quantum thermal bath. These kinetic equations are exact in arbitrary dichotomous perturbation and provide a unified description of both small and large correlation time limits, along with an intermediate case. As an example, the problem of a dissipative two-level system with a dichotomically modulated difference in eigenergies is considered.
The nonequilibrium density matrix technique is utilized to study the incoherent transfer of a quantum particle coupled to a fluctuating environment. The dynamics of the environment is assumed to split into two different types of molecular motions. The first type is associated with low-amplitude vibrations forming a thermal bath (TB). High-amplitude displacements of separated molecular groups define the second type and create stochastic fields for acting on the transferred particle. Specifying the TB by a set of harmonic oscillators and the stochastic fields by a dichotomic process averaged kinetic equations were derived. These equations enable us to construct a rate constants expressions and to find the steady-state populations for a quantum particle. Regimes of enhanced or reduced particle transfer are discussed in detail in relation to the characteristics of the stochastic field and the TB. \textcopyright{} 1996 The American Physical Society.
Kinetic equations of the quantum particle motion in a symmetric dimer are studied for the case of fluctuating site energies and a fluctuating intersite coupling matrix element. Modulations of the site energies are incorporated via quantum fluctuations of a thermal bath whereas the fluctuations of the intersite coupling are taken into account by a stochastic description. In contrast to the quantum fluctuations which are considered in the weak coupling limit, the stochastic fluctuations are included in an exact manner. The exact solution of the averaged kinetic equations are obtained in the case of an Ohmic thermal bath with a white noise spectrum and dichotomous fluctuations of the intersite coupling.
We study the evolution of a system of free fermions in one dimension under the simultaneous effects of coherent tunneling and stochastic Markovian noise. We identify a class of noise terms where a hierarchy of decoupled equations for the correlation functions emerges. In the special case of incoherent, nearest-neighbour hopping the equation for the two-point functions is solved explicitly. The Green's function for the particle density is obtained analytically and a timescale is identified where a crossover from ballistic to diffusive behaviour takes place. The result can be interpreted as a competition between the two types of conduction channels where diffusion dominates on large timescales.